Every member of the Solo family tree in both canon and Legends

Jaina Solo

In the Star Wars Legends continuity, Han and Leia had twins, Jaina and Jacen. Jaina would become one of the most important Star Wars characters of the expanded universe as she grew up, inheriting both her father's piloting ability and her mother's Force sensitivity. Jaina would be a major player during the Yuuzhan Vong invasion as well as the Second Galactic Civil War. 

Jacen Solo

Like Ben Solo in the current continuity, Jacen Solo is the son of Han and Leia who fell to the Dark Side. Jacen Solo spent his younger years learning to be a Jedi Knight alongside his sister, but would eventually turn against her as well as the rest of the family. Jacen took up the title of Darth Caedus as he became a Sith Lord.

Anakin Solo

As the third child of Han and Leia, Anakin Solo was the younger brother of the twins, being born a little over a year after them. The child was originally going to be named Han Solo Jr., but Leia wanted to name the child after her father in an effort to help redeem his name. Like his two older siblings, Anakin Solo trained to be a Jedi Knight and would become pivotal in the Galactic events that happened in the decades following the fall of the Empire. 

Allana Djo Solo

Allana is the daughter of Jacen Solo, and the only known grandchild of Han and Leia. Like most of the other members of her family, Allana possessed a strong connection to the Force. Though in the Legends material that we got before the Disney purchase, she had not received much formal training in the ways of the Jedi. Because the Legends timeline is not moving forward, we'll never know how Allana's story ended up, but in some visions that we know about, she was seen to possibly grow into a Jedi Queen. 

Ania Solo

Star Wars: Legacy was a comic series that began in 2006. It leaped forward in the timeline by a century, showing us the galaxy long after Luke, Han, Leia, and the rest had passed. The main character of the series was a descendant of Luke, but of course a Solo character was going to show up at some point.

The second volume of the era, which began in March of 2013, starred a descendant of Han and Leia named Ania Solo. Ania shared the traits of many of her ancestors. At one point, she was in possession of a lightsaber, but she acquired it through scavenging. She is a good shot and a skilled pilot. The character's story would eventually come to an end when the comic publishing rights for Star Wars went from Dark Horse back to Marvel. Ania is at the end of the Solo family tree in the Legends timeline, but there are still many names if we go in the other direction, looking at who came before Han. 

Jonash and Jaina Solo

Originally, these were the names of Han's parents. While they never appeared in any of the Expanded Universe material, Han would mention them from time to time. We know that the spaceship Jaina's Light, which Han was once in charge of, was named after his mother. Jonash and Jaina disappeared, leaving Han to fend for himself by the time Han was seven. It's not been explicitly stated if they were killed or not, but the way Han has spoken about them the times they were mentioned, it seems like that is a possibility. 

Tiion Solo

Tiion was the aunt of Han Solo and the mother of Thrakan Sal-Slo. She only ever appeared in flashbacks, as her son became a major player in the Star Wars galaxy. 

Thrakan Sal-Solo

Han's older cousin by a few years, Thrakan, would use a hyphenated last name but is still considered to be part of the House of Solo. Thrakan has been everything from a wanted criminal to a head of state. Thrakan was an Empire loyalist which helped to shape his political career. He was well-loved on his home planet of Corellia, though he and Han would have constant issues at many points throughout their lives.  

Denn/Dalla Solo

Two different people could possibly be Han's grandfather, though it's also possible that they could be the same person using two different names. Dalla was a space pirate during the era of the Clone Wars and held a possible claim to the throne of Corellia. Denn lived with his wife and two children and disappeared in a pirate raid. It's possible that Denn was the public persona that allowed Dalla's less than legal activities to thrive, and the pirate raid may have been a result of that dual life. However, again, it is not confirmed that these two are of the same character. 

Tira Gama Solo

Married to Denn Solo, Tira gave birth to the twins Jonash and Tiion shortly before the planet was attacked by pirates. In the attack, Tira took Tiion, and Denn took Jonash, with the two halves of the family never being able to reunite. 

Korol Solo

As we move further back in the timeline, the history of the Solo family tree continues to get murkier. Korol would have been the great-grandfather of Han Solo and claimed to be the great-great-great-great-grandson of a Corellian King. This, if true, would make Han the rightful King of Corellia, though there are conflicting reports (from the same novel) as to whether or not this is a legitimate connection to the throne or merely a claim without evidence. Korol is also the father of Dalla, though the mystery surrounding the connection between Dalla and Denn Solo means that Han's connection to Korol is also tentative. 

Berethron e Solo

Berethron e Solo was the King of Corellia during the Old Republic, a thousand years before the events of the original Star Wars trilogy. If we are to take Korol Solo's claim as a descendant of Berethron e Solo as legitimate, that would make him a direct ancestor of Han Solo as well. 

Jonash e Solo

Three thousand years before the events of the original Star Wars trilogy, Jonash e Solo was the Prince-Admiral of Corellia. Jonash e Solo was the head of the Corellian military during a civil war between two factions of the Galactic Republic at the time. The character was introduced not in a novel or comic but in a reference book, The Essential Guide to Warfare by Jason Fry, part of the Essential Guide series. Jonash e Solo's connection to the later members of the House of Solo was never explored before the characters were all rebranded as part of the Legends Timeline, so it's possible that this character has no connection to the more well-known members of the Solo family. However, given his title as Prince-Admeral and the fact that later Solos held the title of King of Corellia, Jonash e Solo may be the furthest back known member of the Solo bloodline.